Assume that X has a normal distribution, and find the indicated probability.
-The mean is $\mu = 22.0$ and the standard deviation is $\sigma = 2.4$. Find the probability that $\mathrm { X }$ is between $19.7$ and $25.3$.
A)0.7477
B)0.4107
C)0.3370
D)1.0847

Question

Quizplus · Accepted Answer

To find the probability that $X$ is between 19.7 and 25.3, we use the standard normal distribution by converting the given values to Z-scores using the formula $Z = \frac{X - \mu}{\sigma}$. For $X = 19.7$, $Z = \frac{19.7 - 22.0}{2.4} = -0.9583$, and for $X = 25.3$, $Z = \frac{25.3 - 22.0}{2.4} = 1.375$. Looking these Z-scores up in a standard normal distribution table or using a calculator gives us the probability of $X$ being between these two values, which is approximately 0.7477.

Assume That X Has a Normal Distribution, and Find the Indicated